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Properties

Label 1296.4.bk
Level $1296$
Weight $4$
Character orbit 1296.bk
Rep. character $\chi_{1296}(35,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2568$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1296.bk (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).

Total New Old
Modular forms 7848 2616 5232
Cusp forms 7704 2568 5136
Eisenstein series 144 48 96

Trace form

\( 2568 q + 12 q^{2} - 12 q^{4} + 12 q^{5} - 24 q^{7} + 18 q^{8} + O(q^{10}) \) \( 2568 q + 12 q^{2} - 12 q^{4} + 12 q^{5} - 24 q^{7} + 18 q^{8} - 6 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{14} - 12 q^{16} + 36 q^{17} - 6 q^{19} + 474 q^{20} - 12 q^{22} + 24 q^{23} - 24 q^{28} + 12 q^{29} + 12 q^{32} - 60 q^{34} + 18 q^{35} - 6 q^{37} + 12 q^{38} - 12 q^{40} - 12 q^{43} + 18 q^{44} - 6 q^{46} - 24 q^{49} + 6408 q^{50} - 12 q^{52} - 48 q^{55} + 2070 q^{56} + 1770 q^{58} - 3048 q^{59} - 12 q^{61} + 3780 q^{62} - 6 q^{64} + 24 q^{65} - 12 q^{67} - 4206 q^{68} + 2046 q^{70} + 36 q^{71} - 5448 q^{74} - 12 q^{76} + 12 q^{77} - 24 q^{82} + 3672 q^{83} - 762 q^{85} + 8352 q^{86} - 12 q^{88} - 6 q^{91} - 9450 q^{92} - 12 q^{94} - 24 q^{97} + 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)